We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the primal variable through the Lagrange multipliers. This approach has both theoretical and practical advantages. On the one hand, it simplifies the proof of the exponential convergence in the case of smooth, strongly convex problems, with a more straightforward assessment of the convergence rate concerning prior literature. On the other hand, through several examples, we show that the proposed algorithm converges faster than primal-dual gradient dynamics. This paper aims to illustrate these points by thoroughly analyzing the algorithm convergence and discussing some numerical simulations.
A feedback control approach to convex optimization with inequality constraints / Cerone, Vito; Fosson, Sophie M.; Pirrera, Simone; Regruto, Diego. - (2024), pp. 2538-2543. (Intervento presentato al convegno 63rd IEEE Conference on Decision and Control (CDC) tenutosi a Milano (IT) nel December 16-19, 2024) [10.1109/CDC56724.2024.10885825].
A feedback control approach to convex optimization with inequality constraints
Cerone, Vito;Fosson, Sophie M.;Pirrera, Simone;Regruto, Diego
2024
Abstract
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the primal variable through the Lagrange multipliers. This approach has both theoretical and practical advantages. On the one hand, it simplifies the proof of the exponential convergence in the case of smooth, strongly convex problems, with a more straightforward assessment of the convergence rate concerning prior literature. On the other hand, through several examples, we show that the proposed algorithm converges faster than primal-dual gradient dynamics. This paper aims to illustrate these points by thoroughly analyzing the algorithm convergence and discussing some numerical simulations.File | Dimensione | Formato | |
---|---|---|---|
CDC2024_final.pdf
accesso aperto
Tipologia:
2. Post-print / Author's Accepted Manuscript
Licenza:
Pubblico - Tutti i diritti riservati
Dimensione
405.36 kB
Formato
Adobe PDF
|
405.36 kB | Adobe PDF | Visualizza/Apri |
A_feedback_control_approach_to_convex_optimization_with_inequality_constraints.pdf
accesso riservato
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Non Pubblico - Accesso privato/ristretto
Dimensione
474.25 kB
Formato
Adobe PDF
|
474.25 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/2997464